Acoustic wave devices have been used extensively in the art as frequency reference resonators, delay lines, and sensors. The oldest acoustic wave device structure is the parallel plate resonator, which consists of a plate of piezoelectric material having substantially flat and parallel polished surfaces, one or both of which support one or more conducting electrodes. When a voltage signal is applied between the electrodes, stress fields induce elastic deformations of the crystal (strain fields). The deformations of the crystal alter the distribution of charge within the crystal and a net flow of charge (a current) exists. Resonance occurs when the mirror-polished crystal faces are spaced in multiples of a half wavelength, modified for the effects of electrodes and surface contouring.
A more advanced acoustic wave device utilizes surface acoustic waves, surface transverse waves, or acoustic plate modes, collectively known as surface generated acoustic wave (SGAW) devices. This term was defined by John Vetelino (see for example, Theory, design and operation of surface generated acoustic wave sensors, Vetelino et al, Microwave Symposium Digest, 1994., IEEE MTT-S International, 23-27 May 1994 Page(s):505-508 vol. 1) to mean any acoustic wave that is generated at, detected at, and interacts with the surface of the piezoelectric. It includes SAW (SH and Rayleigh), leaky SAW, Love, Lamb, acoustic plate mode, shallow bulk acoustic wave, surface skimming bulk wave, and the like. Briefly, these devices comprise, by way of non-limiting examples, a substrate of piezoelectric material such as quartz, or thin films of piezoelectric material, such as zinc oxide, on a non-piezoelectric substrate. The substrate has at least one active piezoelectric surface area, which is highly polished. Formed on the surface are input and optional output transducers for the purpose of converting input electrical energy to acoustic energy within the substrate and reconverting the acoustic energy to an electric output signal. The input and output transducers frequently comprise interdigital transducers each comprising a plurality of interdigital electrode fingers which are electrically coupled to an input signal, and to an output measurement device respectively. Such transducers are known as IDT (interdigital transducer) and are typically formed by depositing a thin film of electrically conductive material such as aluminum or gold in the desired shape on the active area or by chemically modifying an insulating or semiconducting medium. Electrical potential is coupled to the input transducer and induces mechanical stresses and strains in the piezoelectric substrate. The resultant acoustic waves propagate along the surface of the substrate to the optional output transducer or are reflected back to said input transducer, whereby they are converted to output electrical signals. The waves may propagate along the surface of the crystal (surface modes), or within the bulk of the crystal structure (waveguide modes).
When designing an acoustic wave device, one has to consider the size, number, mass, shape, and connection method of the electrodes, as those parameters significantly affect the behavior of the device. The effects of the electrode design are known in the art and a continuum of properties is well observed in the literature, especially with regards to metal type and thickness. For simplicity, an electrode structure is mechanically insignificant where an acoustic wave traveling under a short-circuited transducer containing mechanically insignificant electrodes would experience no significant reflective coupling into a reverse-traveling wave due to the periodic perturbations from the nominal surface conditions outside the transducer region.
The opposite of mechanically insignificant electrode structure described above, is naturally the mechanically significant electrode structure, meaning that such reflective coupling would be created and enhanced. Generally speaking mechanically significant electrodes are employed to reflect or contain acoustic energy. An arrangement of one or more mechanically significant electrodes can be employed to implement a reflective member of an acoustic wave device, as would be required in a resonator.
The invention relates specifically to acoustic wave resonators based on SGAW. The most commonly used SGAW for resonator structures are surface acoustic wave (SAW) and surface transverse wave (STW); however any SGAW is a candidate and is understood to be considered herein.
Fundamentally a resonator requires two outer reflective elements having reflection, Γi, separated by a transmission element having transmission, Tij. Transmission term T12 defines the magnitude and phase shift of the signal at reflector 1 due to a signal incident from reflector 2 and vice versa. The resonant frequencies of this generalized structure are the zeros of1−Γ1T12T21Γ2and requires the magnitudes of Γi and Tij to all be unity (loss-free) for zeros to occur on the real frequency axis. Practical resonators have finite loss and the zeros lie in the complex plane with a damping term. Minimizing that loss, and therefore the quality factor (Q) of the acoustic resonance, is a designer's high priority.
An acoustic wave resonator may be generically defined as two reflective members separated by a transmission member arranged such that the sum of the phases of the two reflection coefficients and the double transit phase of the intervening transmission member is a multiple of 2π at a desired frequency, namely the so-called resonant frequency. The phase condition mathematically states that the successive echoes within the structure are in phase, creating a standing wave of stored energy. When applied to the mirror surfaces of a polished crystal, this condition yields the well known half-wavelength thick bulk wave resonator. This simplistic view of a resonator neglects the step of injecting and sampling acoustic stored energy by an electrical circuit for the SGAW case.
The polished mirror surface of the bulk wave resonator is impractical in SGAW devices and instead a pseudo-periodic array of reflective elements is employed. The subject matter herein is independent of the myriad means by which reflective elements have been implemented in the past; however the two most common means are etched grooves and metal strips. Dot arrays (etched or metal) have also been demonstrated.
Where specific definitions are needed, a “reflective element” refers to a single feature (etched groove or metal strip, etc.) and a “reflector array” or “reflector” or “grating” refers to an ensemble of said reflective elements. By far the most common implementation is a periodic reflector array having several hundred individual reflective elements with a periodicity that is nominally half that of the intended acoustic wavelength. The most common reflective elements are metal strips with a width of one quarter of the acoustic wavelength and a thickness on the order of 1.5% of the acoustic wavelength. These details are offered by way of illustration and the literature offers many examples of thinner and thicker metal, shallower or deeper grooves, and wider or narrower features. While the most common arrangements employ uniformly periodic reflection, one skilled in the art will realize that there are advantages relative to sidelobe suppression and reduction of bulk wave scattering that may be realized by slightly modulating the periodicity. Therefore a reflector array shall be taken to include a pseudo-periodic array of reflective elements. It is noted that for structures of modulated periodicity, there is a nominal constant periodicity of an idealized periodic structure that will provide the same behavior near the frequencies of interest. This nominal periodicity is a weighted average periodicity and shall be implied to be the “periodicity” describing the structure.
The salient property of a reflective element and of a reflector array is that they remove energy from a traveling acoustic wave and scatter it back into a wave of identical frequency traveling in the opposite direction. One well known effect of asymmetry is that the direction of the phase velocity vector and energy velocity vector are not coincident. The angle between these vectors is known as the power flow angle and it has been long understood that the centerline of the array should nominally follow the energy velocity vector since energy will flow along this vector. In contrast, the individual elements naturally remain perpendicular to the phase velocity vector such that the wave phase is constant across the electrode or reflector. The existence of a power flow angle requires one to further clarify that the reflected signal has energy reflected back along the incident energy velocity vector (centerline of the array) with equal and opposite angle between said centerline and the associated phase velocity. This solution to power flow angle is illustrated in Cho and Williams' FIGS. 13 and 14 in “Numerical Analysis of Doubly Rotated Cut SAW Devices”, Williams and Cho, 1979 IEEE Ultrasonics Symposium. It has long been recognized that such power flow angle compensation is applicable to resonators and impedance elements as well as to delay lines. One sufficiently skilled in the art will recognize that one can equally well slant the electrodes, keeping the energy velocity vector “horizontal” or stagger the electrodes vertically, making the energy velocity vector slant.
A more important property of substrate asymmetry is that the peaks of acoustic energy are displaced from the peaks of electric energy, resulting in a so-called phase shift between the centers of transduction and the centers of reflection in an IDT having mechanically significant electrodes. In the least case this asymmetry incurs increased spurious modes and in the worst case, incurs seriously reduced piezoelectric coupling to the resonator's standing wave. The aim of the present invention is to address this issue. The remaining background material explains the resonator structure and how the asymmetry affects the resonator properties.
The aggregate effect of a large number of periodically spaced reflective elements is to prevent an acoustic wave from traveling unimpeded through the array at a frequency for which the wavelength of the acoustic wave is nearly equal to twice the periodicity of the array. At this so-called Bragg frequency, the reflections from each element in the array are coherent with one another and the wave is completely reflected (in the absence of undesired dissipative losses). Due to the interaction of the incident and reflected waves on each other, this synchronicity is maintained over a band of frequencies near the synchronous or Bragg frequency. The width of the band is determined by the strength of the reflective coupling of the individual elements and is known as the stopband.
The reflection coefficient of an array of electrodes beginning at X=0 and continuing on indefinitely is ideally unity across the stopband and rapidly falls to zero outside the stopband. For a finite number of elements the reflection within the stopband is not unity and the transition region is finite with many sidelobes.
The phase of the reflectivity depends on the reference plane. It is assumed herein that the reference plane is located lambda/4 from the center of the first element and that the array consists of lambda/4 metal strips. This reference plane is chosen so that a reflective array appears to have the same reflection phase from its right and left faces on a symmetric substrate orientation and so that the centers of transduction are located at points of high symmetry (center of gaps or center of electrodes). In this case there is an odd multiple of 90° (π/2 radians) of reflection phase (of the dominant acoustic component) at the Bragg frequency as seen in prior art FIG. 1. Slight numerical error and non-ideal properties inherent in the model lower the Bragg frequency slightly below the simple estimate of FB=V/2P for velocity, V, and period, P. Two other frequencies within the stopband are seen to also exhibit an odd multiple of 90°, one near the lower stopband edge and one near the upper stopband edge.
The required spacing of an intervening transmission medium to obtain an acoustic resonance and standing wave at the Bragg frequency is (N+0.25)P, where P is the wavelength of the acoustic wave at the synchronous frequency. A trivial case having no transducer is indicated in prior art FIG. 2. The associated resonance at synchronous frequency (˜500 MHz) would be accompanied by spurious resonances (˜499 MHz and ˜501 MHz) and potentially near other quadrature points coinciding with reflector sidelobes. The exact locations of such spurious resonances will depend on N, among other factors.
Increasing the spacing would alter the round-trip transmission phase from −180° to a more negative number and subsequently require a less negative reflection phase. This would result a lower resonant frequency, also reducing the phase increase of the longer transmission medium. Shortening the transmission medium would have the opposite effect. One skilled in the art can model such structures and analyze the interaction of the non-linear system of equations governing the resonance condition.
Propagation loss in the transmission member and reflection losses from the finite reflector array determine the quality of the resonator in its unloaded state. The unloaded quality factor, QU, is mathematically defined as the stored energy of the resonator in said standing wave divided by the energy lost per cycle. High quality resonances require very low reflection losses and very low transmission losses.
An acoustic wave resonator is only practical if one is capable of exchanging energy with an electrical circuit, requiring either the transmission member or one or both of the reflection members to also provide a transducer means. The electrical load presented by said electrical circuit represents a loss mechanism to the acoustic stored energy that reduces the effective quality factor. The so-called loaded quality factor, QL, is dependent on the load impedance and is lower than QU for all cases other than open and short circuit conditions.
The transducer means consists of a collection of at least one so-called cell having interdigitated electrodes. In the simplest case each cell is identical and periodic at the transducer period, having a single positive and a single negative electrode. However there are numerous transducer cells known in the art, having lengths equal to the period as well as to harmonics and sub-harmonics of the period. There are also transducers consisting of cells having different lengths, arranged in an ensemble with an average period. Each cell has a physical center, a center of reflection, and a center of transduction. The relative locations of the centers of transduction and reflection within a cell are related to each other by a combination of cell design and substrate properties.
On symmetric orientations a cell having symmetry or anti-symmetry will have a relative phase between transduction and reflection equal to a multiple of a quarter period (90°). Since a translation of the center of transduction by a quarter period can be accomplished by changing the polarity of the assumed reflection coefficient, any multiple of a quarter wavelength may be considered a symmetric arrangement of the centers of transduction and reflection. Asymmetry, as occurs for intentionally asymmetric cells or for symmetric cells on asymmetric orientations of piezoelectric media, alters the design requirements and electrical performance of the resulting acoustic wave device. The present invention discusses methods of compensating device performance for the consequences of having such asymmetric cells, in which the centers of transduction and centers of reflection are displaced from the high symmetry conditions, denoted herein as an asymmetry between its centers of transduction and its centers of reflection.
The earliest SAW devices sought to apply finite impulse response (FIR) filter theory to a simple delay line structure consisting of an input transducer and an output transducer. The structures diligently avoided reflections and taught toward the use of mechanically insignificant electrode structures. Delay lines and finite impulse response filters were found to require electrical mismatching in order to suppress undesired time domain echoes. Means were sought to overcome this electrical inefficiency and, for narrow-band applications, resonator filters were developed.
It is therefore no surprise that the earliest SAW resonators were implemented by placing arrays of mechanically significant electrodes as reflector arrays on either side of such reflectionless IDTs as in U.S. Pat. No. 3,716,809. The resulting devices were found to have numerous resonant frequencies due to the long acoustic length of the transmission member between the reflective members U.S. Pat. No. 3,961,293.
Shreve U.S. Pat. No. 4,144,507 overcame this problem of spurious modes by incorporating the transduction means directly into the reflective member. The most significant of the remaining spurious modes were addressed by selective placement of transducer nulls by Wright U.S. Pat. No. 4,616,197. However, both Shreve and Wright relied on a finite break in the periodicity of the structure. Such breaks are known to result in energy scattering into the bulk of the substrate and are generally considered undesirable.
Prior art FIG. 3 illustrates a generic one port resonator in which the interdigital transducer 301 is located between reflector arrays 302 and 303. In general, there may also be finite phase shift regions 304 and 305. Also generally speaking, the periods of the IDT (P1) need not be equal to the equal periods of the two reflectors (P2=P3); however all of the periods are nearly equal to each other and to half the acoustic wavelength at or near the resonant frequency.
Prior art FIG. 4A illustrates a situation in which the transmission element is simply an interdigital transducer without phase skips. At the synchronous (Bragg) frequency of the structure, FB, the transducer has an acoustic phase shift equal to a multiple of 2π; however the reflectivity of each of the end reflectors is π/2 at this frequency if P1=P2=P3 as is typical of the prior art. The structure of prior art FIG. 4A will not satisfy the resonant conditions at the center frequency if the periods are all equal. If one examines the frequency dependence of the grating, one sees that the reflection magnitude is essentially constant over a band of frequencies known as the stopband. These are the frequencies for which the forward and reverse traveling waves are reflectively coupled into each other and the width of this band is determined by the reflectivity per wavelength of the grating structure, κ. Between the stopband edge frequencies, FB(1±κ/2π), there is typically a range of reflection phase from at least −π to π. The structure illustrated in prior art FIG. 4A typically exhibits a resonance closer to the stopband edges when the period is constant throughout the structure.
Avramov (I. D. Avramov, “High Q metal strip SSBW resonators using a SAW design”, IEEE Trans. UFFC., vol. 37, pp. 530-534, 1990), has used this structure to maximize dispersive energy trapping in STW resonators. One drawback to this approach for frequency control applications is in the manufacturing yield. The resonant frequency of the device is dependent on FB and on κ. Both of these parameters vary with metal thickness and line-to-space ratio. The further the resonant frequency is removed from FB the worse this variability is.
In the early days of resonator manufacture, the photolithographic process was near its limitations and it was necessary to operate the resonator at FB to maximize yield in cost-sensitive, high volume applications as discussed in “Coupling-Of-Modes Analysis Of Saw Devices”, V. Plessky, International Journal of High Speed Electronics and Systems. In order to accomplish this while maintaining a synchronous structure (a structure in which the local period within each element is constant other than in one or more discrete steps and in which reflectivity of the IDT was in phase with that of at least one neighboring reflector) it is necessary to insert an additional π/2 of transmission phase, requiring an excess P/4 of transmission line. The requisite phase could be implemented in phase shift region 304 or 305 or through a combination of the two. If IDT 301 of prior art FIG. 3 is selected to be reflectionless, then the only relevance of the relative lengths of phase shifters 304 and 305 is the synchronization of the standing wave between the reflectors with the transduction centers of the IDT. In the case wherein the IDT is reflective, there will exist second order interactions of the reflectivity of the IDT and the actual reflectors; however the primary constraint will continue to be maximizing electrical efficiency.
The IDT 401 in prior art FIG. 4B is placed synchronous with the left reflector 402. The left phase shift 404 is zero and the right phase shift 405 is π/2. This additional phase shift defines a cavity feature to which the wave is trapped and the stored energy decreases with distance from the cavity. It should be noted that the sinusoidal signal is meant to convey the acoustic wave's associated electrical potential. It is therefore noted that at the resonant frequency, FB, the transducer is no longer located in the ideal phase relationship to the stored energy, resulting in decreased electrical performance. Furthermore there exists increased electrical efficiency at frequencies below the desired resonance, resulting in a spurious resonance below the desired frequency. Finally, there exists a null at a frequency slightly above resonance where the standing wave is located exactly π/2 away from the transducer's optimum sampling locations. In addition to the resonant condition established above, it is therefore beneficial that the transducers be located in the transmission element in such a way that the centers of transduction of the transducer align more or less synchronous with the peaks of the standing wave of stored energy in the resonator.
Prior art FIG. 4C shows a two-port resonator wherein each IDT is synchronous with the adjacent reflector. Interconnecting the transducers results in the composite transducer of U.S. Pat. No. 4,616,197. The use of a short, frequency-shifted grating with an effective length of (M+0.25) to alleviate the bulk wave scattering of the finite gap is known in the art. This so-called hiccup transducer places the cavity in the middle of the transducer. This adds a second null due to the array factor at the peak of coupling of the individual electrodes and allows the resonance to be at the Bragg frequency. One-port resonators sold by R F Monolithics in the mid 1980's e.g., the ROxxxx family part numbers employed the structure of prior art FIG. 4C in which the π/2 shift was implemented as six “periods” of “reflector array” with their period decreased by 5.75/6. The effect was to implement the requisite phase shift with no break in local structure and only a modest discontinuity in the periodicity of the reflectors. Other arrangements are well known in the art and certain embodiments are disclosed by Bauer in U.S. Pat. No. 6,420,946.
As an alternative to Wright, the electrical performance of a resonator can be improved by inserting less than the full π/2 of phase shift, bringing the resonance below the Bragg frequency and coincident with the peak of electrical coupling. The improvement in electrical performance is obtained at the expense of manufacturing frequency tolerance; however modern lithography allows good yield.
Regardless of the exact length, the skip in periodicity creates a discontinuity that results in conversion of SAW energy into bulk wave energy. Another approach is to slightly alter the period of the transducer as disclosed by Uno in U.S. Pat. No. 4,387,355. Such a resonator employs the fact that mechanically significant electrodes within the transducer distort its electrical response and create a peak of electromechanical coupling related to either the lower or upper edge of the reflective stopband. By placing the coupling resonance of the IDT at the intended resonant frequency of the structure, optimization occurs. Lowering the transducer period raises the frequency at which the electrodes are optimally converting energy and alters the phase shift through the transducer. The structure resonates at a frequency which is not necessarily the synchronous (Bragg) frequency of either the IDT or the reflectors. The prior art approach is illustrated in FIG. 5. IDT 501 has period P1 less than the equal periods, P2=P3, of reflectors 502 and 503.
The aforementioned resonator structures were all implemented on piezoelectric substrates of high symmetry with the exception of U.S. Pat. No. 4,731,595, to Wright. Such substrates have a well defined relationship between the phase of reflection and phase of transduction as being an integral multiple of π/2. On substrates of significant asymmetry this phase relationship can have any value and for many of the prior art structures disclosed above this results in a need to shift the location of at least one transducer to account for this phase shift, as in Wright, U.S. Pat. No. 4,731,595. Prior art FIG. 3 of Wright illustrates the effect of a π/4 phase shift between the acoustic standing wave (solid) and associated acoustic potential (dotted) in a synchronous resonator as would result from U.S. Pat. No. 4,144,507 or U.S. Pat. No. 4,616,197, resulting in a null of the electrical coupling at the desired resonant frequency (FIG. 4 of U.S. Pat. No. 4,731,595).
The structure of U.S. Pat. No. 4,731,595 offers a potential solution that has been employed commercially; however the structure has several limitations. One problem is the discrete physical break in periodicity that is known to result in energy scattering into the bulk of the crystal. While this effect is dramatically more severe in surface transverse wave (STW) resonators, it is also a significant limitation to QU in SAW resonators. A more significant problem is that the IDT has its peak electromechanical coupling efficiency at the upper and lower edges of the stopband, resulting in substantial coupling to two spurious modes, as predicted above, and a relative decrease of the electrical efficiency of the structure at its resonant frequency. A similar effect occurs in the structure of U.S. Pat. No. 4,387,355; however the decrease of electrical efficiency is less complete.